Maths With Out Coursework (2012)

7/28/2019 Maths With Out Coursework (2012)

1/46

*This syllabus is accredited for use in England, Wales and Northern Ireland as a Cambridge

International Level 1/Level 2 Certificate.

Syllabus

Cambridge IGCSE MathematicsCambridge International Certificate*

Syllabus code 0580

For examination in June and November 2012

Cambridge IGCSE Mathematics (with coursework)Syllabus code 0581

For examination in June and November 2012


2/46


3/46

Contents

Cambridge IGCSE Mathematics

Syllabus code 0580

Cambridge IGCSE Mathematics (with coursework)

Syllabus code 0581

Note: The Mathematics 0580 syllabus is accredited for use in England, Wales and Northern Ireland.

1. Introduction ..................................................................................... 21.1 Why choose Cambridge?

1.2 Why choose Cambridge IGCSE Mathematics?

1.3 Cambridge International Certificate of Education (ICE)

1.4 UK schools1.5 How can I find out more?

2. Assessment at a glance .................................................................. 5

3. Syllabus aims and objectives ...........................................................73.1 Syllabus aims

3.2 Assessment objectives and their weighting in the exam papers

4. Curriculum content ........................................................................ 10

4.1 Grade descriptions

5. Coursework: guidance for centres ................................................ 215.1 Procedure

5.2 Selection of Coursework assignments

5.3 Suggested topics for Coursework assignments

5.4 Controlled elements

6. Coursework assessment criteria ................................................... 246.1 Scheme of assessment for Coursework assignments

6.2 Moderation

Cambridge IGCSE Mathematics 0580/0581. Examination in June and November 2012.

UCLES 2009


4/46


7. Appendix A: ................................................................................... 317.1 Resources

Individual candidate record card

Coursework assessment summary form

8. Appendix B: Additional information ............................................... 37

9. Appendix C: Additional information Cambridge InternationalCertificates .................................................................................... 39


5/46


6/46

2


1. Introduction

1.1 Why choose Cambridge?University of Cambridge International Examinations (CIE) is the worlds largest provider of international

qualifications. Around 1.5 million students from 150 countries enter Cambridge examinations every year.

What makes educators around the world choose Cambridge?

Recognition

Cambridge IGCSE is internationally recognised by schools, universities and employers as equivalent to UKGCSE. Cambridge IGCSE is excellent preparation for A/AS Level, the Advanced International Certificate of

Education (AICE), US Advanced Placement Programme and the International Baccalaureate (IB) Diploma.

Learn more at www.cie.org.uk/recognition .

SupportCIE provides a world-class support service for teachers and exams officers. We offer a wide range of

teacher materials to Centres, plus teacher training (online and face-to-face) and student support materials.

Exams officers can trust in reliable, efficient administration of exams entry and excellent, personal support

from CIE Customer Services. Learn more at www.cie.org.uk/teachers.

Excellence in educationCambridge qualifications develop successful students. They not only build understanding and knowledge

required for progression, but also learning and thinking skills that help students become independent

learners and equip them for life.

Not-for-profit, part of the University of CambridgeCIE is part of Cambridge Assessment, a not-for-profit organisation and part of the University of Cambridge.

The needs of teachers and learners are at the core of what we do. CIE invests constantly in improving its

qualifications and services. We draw upon education research in developing our qualifications.


7/46

3


1. Introduction

1.2 Why choose Cambridge IGCSE Mathematics?Cambridge IGCSE Mathematics is accepted by universities and employers as proof of mathematical

knowledge and understanding. Successful IGCSE Mathematics candidates gain lifelong skills, including:

the development of their mathematical knowledge;

confidence by developing a feel for numbers, patterns and relationships;

an ability to consider and solve problems and present and interpret results;

communication and reason using mathematical concepts;

a solid foundation for further study.

Cambridge IGCSE Mathematics is structured with a Coursework option and is ideal for candidates of all

abilities. There are a number of mathematics syllabuses at both IGCSE and A & AS Level offered by CIE

further information is available on the CIE website at www.cie.org.uk.

1.3 Cambridge International Certificate of Education (ICE)Cambridge ICE is the group award of the International General Certificate of Secondary Education (IGCSE).

It requires the study of subjects drawn from the five different IGCSE subject groups. It gives schools the

opportunity to benefit from offering a broad and balanced curriculum by recognising the achievements of

students who pass examinations in at least seven subjects, including two languages, and one subject from

each of the other subject groups.

The Cambridge portfolio of IGCSE qualifications provides a solid foundation for higher level courses such

as GCE A and AS Levels and the International Baccalaureate Diploma as well as excellent preparation for

employment.

A wide range of IGCSE subjects is available and these are grouped into five curriculum areas. Mathematics

falls into Group IV, Mathematics.

Learn more about ICE at www.cie.org.uk/qualifications/academic/middlesec/ice.


8/46

4


1. Introduction

1.4 UK schoolsCambridge IGCSE Mathematics (without coursework) is accredited for use in England, Wales and Northern

Ireland. Information on the accredited version of this syllabus can be found in the appendix to this

document.

1.5 How can I find out more?

If you are already a Cambridge CentreYou can make entries for this qualification through your usual channels, e.g. CIE Direct. If you have any

queries, please contact us at [email protected] .

If you are not a Cambridge CentreYou can find out how your organisation can become a Cambridge Centre. Email us at

[email protected] . Learn more about the benefits of becoming a Cambridge Centre at

www.cie.org.uk.


9/46

5


2. Assessment at a glance

Cambridge IGCSE Mathematics

Syllabus code 0580

Cambridge IGCSE Mathematics (with coursework)

Syllabus code 0581

Syllabus 0580 (without coursework)

Core curriculum

Grades available: CG

Extended curriculum

Grades available: A*E

Paper 1 1 hour

Short-answer questions.

Candidates should answer each question.

Weighting: 35%

Paper 2 1 hours



Weighting: 35%

Paper 3 2 hours

Structured questions.


Weighting: 65%

Paper 4 2 hours



Weighting: 65%

Syllabus 0581 (with coursework)

Core curriculum

Grades available: CG

Extended curriculum

Grades available: A*E

Paper 1 1 hour


Candidates should answer each question.Weighting: 30%

Paper 2 1 hours


Candidates should answer each question.Weighting: 30%

Paper 3 2 hours



Weighting: 50%

Paper 4 2 hours



Weighting: 50%

Paper 5

Coursework.

Weighting: 20%

Paper 6

Coursework.

Weighting: 20%

Candidates who enter for the accredited version of this syllabus may only enter for Mathematics

(without coursework)


10/46

6


2. Assessment at a glance

Candidates should have an electronic calculator for all papers, possibly used in conjunction with four-

figure tables for trigonometric functions. Algebraic or graphical calculators are not permitted. Three

significant figures will be required in answers except where otherwise stated.

Candidates should use the value of from their calculators if their calculator provides this. Otherwise,they should use the value of 3.142 given on the front page of the question paper only.

Tracing paper may be used as an additional material for each of the written papers.

For syllabus 0581, the Coursework components (papers 5 and 6) will be assessed by the teacher using

the criteria given in this syllabus. The work will then be externally moderated by CIE. Teachers may not

undertake school-based assessment of Coursework without the written approval of CIE. This will only

be given to teachers who satisfy CIE requirements concerning moderation and who have undertaken

special training in assessment before entering candidates. CIE offers schools in-service training via the

Coursework Training Handbook.

For 0581, a candidates Coursework grade cannot lower his or her overall result. Candidates entered for

Syllabus 0581 are graded first on Components 1+3+5 or 2+4+6 and then graded again on Components

1+3 or 2+4. If the grade achieved on the aggregate of the two written papers alone is higher then this

replaces the result achieved when the Coursework component is included. In effect, no candidate is

penalised for taking the Coursework component.

AvailabilityThis syllabus is examined in the May/June examination session and the October/November examination

session.

0580 is available to private candidates. 0581 is not available to private candidates.

Combining this with other syllabusesCandidates can combine these syllabuses in an examination session with any other CIE syllabus, except:

syllabuses with the same title at the same level

0607 IGCSE International Mathematics

Please note that IGCSE, Cambridge International Level 1/Level 2 Certificates and O Level syllabuses are at

the same level.


11/46

7


3. Syllabus aims and objectives

3.1 Syllabus aimsThe aims of the curriculum are the same for all candidates. The aims are set out below and describe the

educational purposes of a course in Mathematics for the IGCSE examination. They are not listed in order of

priority.

The aims are to enable candidates to:

1. develop their mathematical knowledge and oral, written and practical skills in a way which encourages

confidence and provides satisfaction and enjoyment;

2. read mathematics, and write and talk about the subject in a variety of ways;

3. develop a feel for number, carry out calculations and understand the significance of the results obtained;

4. apply mathematics in everyday situations and develop an understanding of the part which mathematics

plays in the world around them;

5. solve problems, present the solutions clearly, check and interpret the results;

6. develop an understanding of mathematical principles;

7. recognise when and how a situation may be represented mathematically, identify and interpret relevant

factors and, where necessary, select an appropriate mathematical method to solve the problem;

8. use mathematics as a means of communication with emphasis on the use of clear expression;9. develop an ability to apply mathematics in other subjects, particularly science and technology;

10. develop the abilities to reason logically, to classify, to generalise and to prove;

11. appreciate patterns and relationships in mathematics;

12. produce and appreciate imaginative and creative work arising from mathematical ideas;

13. develop their mathematical abilities by considering problems and conducting individual and co-operative

enquiry and experiment, including extended pieces of work of a practical and investigative kind;

14. appreciate the interdependence of different branches of mathematics;

15. acquire a foundation appropriate to their further study of mathematics and of other disciplines.


12/46

8



3.2 Assessment objectives and their weighting in the

exam papersThe two assessment objectives in Mathematics are:

A Mathematical techniques

B Applying mathematical techniques to solve problems

A description of each assessment objective follows.

A Mathematical techniquesCandidates should be able to:

1. organise, interpret and present information accurately in written, tabular, graphical and diagrammatic

forms;

2. perform calculations by suitable methods;

3. use an electronic calculator and also perform some straightforward calculations without a calculator;

4. understand systems of measurement in everyday use and make use of them in the solution of

problems;

5. estimate, approximate and work to degrees of accuracy appropriate to the context and convert between

equivalent numerical forms;

6. use mathematical and other instruments to measure and to draw to an acceptable degree of accuracy;

7. interpret, transform and make appropriate use of mathematical statements expressed in words or

symbols;

8. recognise and use spatial relationships in two and three dimensions, particularly in solving problems;

9. recall, apply and interpret mathematical knowledge in the context of everyday situations.

B Applying mathematical techniques to solve problemsIn questions which are set in context and/or which require a sequence of steps to solve, candidates should

be able to:

10. make logical deductions from given mathematical data;

11. recognise patterns and structures in a variety of situations, and form generalisations;

12. respond to a problem relating to a relatively unstructured situation by translating it into an appropriately

structured form;

13. analyse a problem, select a suitable strategy and apply an appropriate technique to obtain its solution;

14. apply combinations of mathematical skills and techniques in problem solving;

15. set out mathematical work, including the solution of problems, in a logical and clear form usingappropriate symbols and terminology.


13/46

9



Weighting of assessment objectives

The relationship between the assessment objectives and the scheme of assessment is set out in the tables

below.

Paper 1

(marks)

Paper 2

(marks)

Paper 3

(marks)

Paper 4

(marks)

A: Mathematical techniques 4248 2835 7888 5265

B: Applying mathematical techniques

to solve problems814 3542 1626 6578

Core assessment Extended assessment

A: Mathematical techniques 7585% 4050%

B: Applying mathematical techniques

to solve problems1525% 5060%

The relationship between the main topic areas of Mathematics and the assessment is set out in the table

below.

Number AlgebraSpace &

shape

Statistics &

probability

Core (Papers 1 & 3) 3035% 2025% 3035% 1015%

Extended (Papers 2 & 4) 1520% 35-40% 3035% 1015%


14/46

10


4. Curriculum content

Candidates may follow either the Core curriculum only or the Extended curriculum which involves

both the Core and Supplement. Candidates aiming for Grades A*C should follow the Extended

Curriculum.

Centres are reminded that the study of mathematics offers opportunities for the use of ICT, particularly

spreadsheets and graph-drawing packages. For example, spreadsheets may be used in the work on

Percentages (section 11), Personal and household finance (section 15), Algebraic formulae (section 20),

Statistics (section 33), etc. Graph-drawing packages may be used in the work on Graphs in practical

situations (section 17), Graphs of functions (section 18), Statistics (section 33), etc. It is important to note

that use or knowledge of ICT will not be assessed in the examination papers.

Centres are also reminded that, although use of an electronic calculator is permitted on all examination

papers, candidates should develop a full range of mental and non-calculator skills during the course of study.

Questions demonstrating the mastery of such skills may be asked in the examination.

As well as demonstrating skill in the following techniques, candidates will be expected to apply them in the

solution of problems.

1. Number, set notation and language

Core

Identify and use natural numbers, integers (positive,

negative and zero), prime numbers, square numbers,

common factors and common multiples, rational and

irrational numbers

(e.g. , 2 ), real numbers; continue a given number

sequence; recognise patterns in sequences and

relationships between different sequences, generalise to

simple algebraic statements (including expressions for

the nth term) relating to such sequences.

Supplement

Use language, notation and Venn diagrams to describe

sets and represent relationships between sets as

follows:

Definition of sets, e.g.

A = {x: xis a natural number}

B= {(x,y): y= mx+ c}

C= {x: aYxYb}

D= {a, b, c, }

Notation

Number of elements in set A n(A)

is an element of

is not an element of

Complement of set A A

The empty set

Universal set

A is a subset of B AB

A is a proper subset of B AB

A is not a subset of B AB

A is not a proper subset of B AB

Union of A and B AB

Intersection of A and B AB


15/46

11



2. Squares and cubes

Core

Calculate squares, square roots, cubes and cube roots of

numbers.

3. Directed numbers

Core

Use directed numbers in practical situations (e.g.

temperature change, flood levels).

4. Vulgar and decimal fractions and percentages

Core

Use the language and notation of simple vulgar and

decimal fractions and percentages in appropriate

contexts; recognise equivalence and convert between

these forms.

5. Ordering

CoreOrder quantities by magnitude and demonstrate

familiarity with the symbols

=, , K, I, [ ,Y

6. Standard form

Core

Use the standard form A 10n where n is a positive or

negative integer, and 1 Y A I=10

7. The four rules

CoreUse the four rules for calculations with whole numbers,

decimal fractions and vulgar (and mixed) fractions,

including correct ordering of operations and use of

brackets.

8. Estimation

Core

Make estimates of numbers, quantities and lengths,

give approximations to specified numbers of significant

figures and decimal places and round off answers to

reasonable accuracy in the context of a given problem.


16/46

12



9. Limits of accuracy

Core

Give appropriate upper and lower bounds for data given

to a specified accuracy (e.g. measured lengths).

Supplement

Obtain appropriate upper and lower bounds to solutions

of simple problems (e.g. the calculation of the perimeter

or the area of a rectangle) given data to a specified

accuracy.

10. Ratio, proportion, rate

Core

Demonstrate an understanding of the elementary ideas

and notation of ratio, direct and inverse proportion and

common measures of rate; divide a quantity in a given

ratio; use scales in practical situations; calculate average

speed.

Supplement

Express direct and inverse variation in algebraic terms

and use this form of expression to find unknown

quantities; increase and decrease a quantity by a given

ratio.

11. Percentages

Core

Calculate a given percentage of a quantity; express

one quantity as a percentage of another; calculatepercentage increase or decrease.

Supplement

Carry out calculations involving reverse percentages,

e.g. finding the cost price given the selling price and thepercentage profit.

12. Use of an electronic calculator

Core

Use an electronic calculator efficiently; apply appropriate

checks of accuracy.

13. Measures

Core

Use current units of mass, length, area, volume and

capacity in practical situations and express quantities in

terms of larger or smaller units.

14. Time

Core

Calculate times in terms of the 24-hour and

12-hour clock; read clocks, dials and timetables.

15. Money

Core

Calculate using money and convert from one currency to

another.


17/46

13



16. Personal and household finance

Core

Use given data to solve problems on personal and

household finance involving earnings, simple interest and

compound interest (knowledge of compound interest

formula is not required), discount, profit and loss; extract

data from tables and charts.

17. Graphs in practical situations

Core

Demonstrate familiarity with Cartesian co-ordinates in

two dimensions, interpret and use graphs in practical

situations including travel graphs and conversion graphs,

draw graphs from given data.

Supplement

Apply the idea of rate of change to easy kinematics

involving distance-time and speed-time graphs,

acceleration and deceleration; calculate distance travelled

as area under a linear speed-time graph.

18. Graphs of functions

Core

Construct tables of values for functions of the form

ax+ b, x2

+ ax+ b, a/x(x 0) where a and bareintegral constants; draw and interpret such graphs; find

the gradient of a straight line graph; solve linear and

quadratic equations approximately by graphical methods.

Supplement

Construct tables of values and draw graphs for functions

of the form axn

where a is a rational constant andn = 2, 1, 0, 1, 2, 3 and simple sums of not more

than three of these and for functions of the form ax

where a is a positive integer; estimate gradients of

curves by drawing tangents; solve associated equations

approximately by graphical methods.

19. Straight line graphs

Core

Interpret and obtain the equation of a straight line graph

in the form y= mx+ c; determine the equation of a

straight line parallel to a given line.

Supplement

Calculate the gradient of a straight line from the

co-ordinates of two points on it; calculate the length

and the co-ordinates of the midpoint of a straight line

segment from the co-ordinates of its end points.

20. Algebraic representation and formulae

Core

Use letters to express generalised numbers and express

basic arithmetic processes algebraically, substitute

numbers for words and letters in formulae; transform

simple formulae; construct simple expressions and set

up simple equations.

Supplement

Construct and transform more complicated formulae and

equations.


18/46

14



21. Algebraic manipulation

Core

Manipulate directed numbers; use brackets and extract

common factors.

SupplementExpand products of algebraic expressions; factorise

where possible expressions of the form

ax+ bx+ kay+ kby, a2x2 b2y2; a2 + 2ab+ b2;

ax2 + bx+ c

manipulate algebraic fractions, e.g.

2

4

3

+

xx

,

( )2

53

3

2

xx

,

3

5

4

3 aba ,

10

9

4

3 aa ,

3

2

2

1

+

xx

factorise and simplify expressions such as

62

2

2

2

+

xx

xx

22. Functions

Supplement

Use function notation, e.g. f(x) = 3x 5,

f: xa3x 5 to describe simple functions, and the

notation f1(x) to describe their inverses; form composite

functions as defined by gf(x) = g(f(x))

23. Indices

Core

Use and interpret positive, negative and zero indices.

Supplement

Use and interpret fractional indices,

e.g. solve 32x

= 2

24. Solutions of equations and inequalities

Core

Solve simple linear equations in one unknown; solve

simultaneous linear equations in two unknowns.

Supplement

Solve quadratic equations by factorisation, completing

the square or by use of the formula; solve simple linear

inequalities.

25. Linear programming

Supplement

Represent inequalities graphically and use this

representation in the solution of simple linear

programming problems (the conventions of using broken

lines for strict inequalities and shading unwanted regions

will be expected).


19/46

15



26. Geometrical terms and relationships

Core

Use and interpret the geometrical terms: point, line,

parallel, bearing, right angle, acute, obtuse and reflex

angles, perpendicular, similarity, congruence; use and

interpret vocabulary of triangles, quadrilaterals, circles,

polygons and simple solid figures including nets.

Supplement

Use the relationships between areas of similar triangles,

with corresponding results for similar figures and

extension to volumes and surface areas of similar solids.

27. Geometrical constructions

Core

Measure lines and angles; construct a triangle given

the three sides using ruler and pair of compasses only;

construct other simple geometrical figures from given

data using protractors and set squares as necessary;

construct angle bisectors and perpendicular bisectors

using straight edges and pair of compasses only; read

and make scale drawings.

28. Symmetry

Core

Recognise rotational and line symmetry (including

order of rotational symmetry) in two dimensions and

properties of triangles, quadrilaterals and circles directly

related to their symmetries.

Supplement

Recognise symmetry properties of the prism (including

cylinder) and the pyramid (including cone); use the

following symmetry properties of circles:

(a) equal chords are equidistant from the centre(b) the perpendicular bisector of a chord passes through

the centre

(c) tangents from an external point are equal in length.29. Angle properties

Core

Calculate unknown angles using the following

geometrical properties:

(a) angles at a point(b) angles at a point on a straight line and intersecting

straight lines

(c) angles formed within parallel lines(d) angle properties of triangles and quadrilaterals(e) angle properties of regular polygons(f) angle in a semi-circle(g) angle between tangent and radius of a circle.

Supplement

Use in addition the following geometrical properties:

(a) angle properties of irregular polygons(b) angle at the centre of a circle is twice the angle at

the circumference

(c) angles in the same segment are equal(d) angles in opposite segments are supplementary;

cyclic quadrilaterals.


20/46

16



30. Locus

Core

Use the following loci and the method of intersecting loci

for sets of points in two dimensions:

(a) which are at a given distance from a given point(b) which are at a given distance from a given straight

line(c) which are equidistant from two given points(d) which are equidistant from two given intersecting

straight lines.

31. Mensuration

Core

Carry out calculations involving the perimeter and area of

a rectangle and triangle, the circumference and area of

a circle, the area of a parallelogram and a trapezium, the

volume of a cuboid, prism and cylinder and the surface

area of a cuboid and a cylinder.

Supplement

Solve problems involving the arc length and sector area

as fractions of the circumference and area of a circle, the

surface area and volume of a sphere, pyramid and cone

(given formulae for the sphere, pyramid and cone).

32. Trigonometry

Core

Interpret and use three-figure bearings measured

clockwise from the North (i.e. 000360);

apply Pythagoras theorem and the sine, cosine and

tangent ratios for acute angles to the calculation of a

side or of an angle of a right-angled triangle (angles will

be quoted in, and answers required in, degrees and

decimals to one decimal place).

Supplement

Solve trigonometrical problems in two dimensions

involving angles of elevation and depression; extend sine

and cosine values to angles between 90 and 180; solve

problems using the sine and cosine rules for any triangle

and the formula

area of triangle =21 absin C,

solve simple trigonometrical problems in three

dimensions including angle between a line and a plane.

33. Statistics

Core

Collect, classify and tabulate statistical data; read,

interpret and draw simple inferences from tables and

statistical diagrams; construct and use bar charts, pie

charts, pictograms, simple frequency distributions,

histograms with equal intervals and scatter diagrams

(including drawing a line of best fit by eye); understand

what is meant by positive, negative and zero correlation;

calculate the mean, median and mode for individual and

discrete data and distinguish between the purposes for

which they are used; calculate the range.

Supplement

Construct and read histograms with equal and unequal

intervals (areas proportional to frequencies and vertical

axis labelled 'frequency density'); construct and use

cumulative frequency diagrams; estimate and interpret

the median, percentiles, quartiles and inter-quartile

range; calculate an estimate of the mean for grouped and

continuous data; identify the modal class from a grouped

frequency distribution.


21/46

17



34. Probability

Core

Calculate the probability of a single event as either a

fraction or a decimal (not a ratio); understand and use

the probability scale from 0 to 1; understand that: the

probability of an event occurring = 1 the probability

of the event not occurring; understand probability in

practice, e.g. relative frequency.

Supplement

Calculate the probability of simple combined events, using

possibility diagrams and tree diagrams where appropriate

(in possibility diagrams outcomes will be represented by

points on a grid and in tree diagrams outcomes will be

written at the end of branches and probabilities by the side

of the branches).

35. Vectors in two dimensions

Core

Describe a translation by using a vector represented by

e.g.

y

x

, ABor a;

add and subtract vectors; multiply a vector by a scalar.

Supplement

Calculate the magnitude of a vector

y

x

as 22 yx + .

(Vectors will be printed as ABor a and their magnitudes

denoted by modulus signs, e.g. AB or a. In theiranswers to questions candidates are expected to indicate

a in some definite way, e.g. by an arrow or by underlining,

thus ABor a)

Represent vectors by directed line segments; use the sumand difference of two vectors to express given vectors in

terms of two coplanar vectors; use position vectors

36. Matrices

Supplement

Display information in the form of a matrix of any order;

calculate the sum and product (where appropriate) of two

matrices; calculate the product of a matrix and a scalar

quantity; use the algebra of 2 2 matrices including the

zero and identity 2 2 matrices; calculate the determinant

and inverse A1 of a non-singular matrix A

37. Transformations

Core

Reflect simple plane figures in horizontal or vertical

lines; rotate simple plane figures about the origin,

vertices or midpoints of edges of the figures, through

multiples of 90; construct given translations and

enlargements of simple plane figures; recognise

and describe reflections, rotations, translations and

enlargements.

Supplement

Use the following transformations of the

plane: reflection (M); rotation (R); translation (T);

enlargement (E); shear (H); stretch (S) and their

combinations

(if M(a) = band R(b) = cthe notation RM(a) = cwill be

used; invariants under these transformations may be

assumed.)

Identify and give precise descriptions of transformations

connecting given figures; describe transformations using

co-ordinates and matrices (singular matrices are excluded).


22/46

18



4.1 Grade descriptionsGrade Descriptions are provided to give a general indication of the standards of achievement likely to have

been shown by candidates awarded particular grades. The grade awarded will depend in practice upon the

extent to which the candidate has met the assessment objectives overall. Shortcomings in some aspects of

a candidates performance in the examination may be balanced by a better performance in others.

Grade F

At this level, candidates are expected to identify and obtain necessary information. They would be expected

to recognise if their results to problems are sensible. An understanding of simple situations should enable

candidates to describe them, using symbols, words and diagrams. They draw simple, basic conclusions with

explanations where appropriate.

With an understanding of place value, candidates should be able to perform the four rules on positive

integers and decimal fractions (one operation only) using a calculator where necessary. They should be

able to convert between fractions, decimals and percentages for the purpose of comparing quantities

between 0 and 1 in a variety of forms, and reduce a fraction to its simplest form. Candidates should

appreciate the idea of direct proportion and the solution of simple problems involving ratio should be

expected. Basic knowledge of percentage is needed to apply to simple problems involving percentage

parts of quantities. They need to understand and apply metric units of length, mass and capacity,

together with conversion between units in these areas of measure. The ability to recognise and continue

a straightforward pattern in sequences and understand the terms multiples, factors and squares is

needed as a foundation to higher grade levels of applications in the areas of number and algebra.

At this level, the algebra is very basic involving the construction of simple algebraic expressions,

substituting numbers for letters and evaluating simple formulae. Candidates should appreciate how a

simple linear equation can represent a practical situation and be able to solve such equations.

Knowledge of names and recognition of simple plane figures and common solids is basic to an

understanding of shape and space. This will be applied to the perimeter and area of a rectangle and

other rectilinear shapes. The skill of using geometrical instruments, ruler, protractor and compasses is

required for applying to measuring lengths and angles and drawing a triangle given three sides.

Candidates should be familiar with reading data from a variety of sources and be able to extract data

from them, in particular timetables. The tabulation of the data is expected in order to form frequency

tables and draw a bar chart. They will need the skill of plotting given points on a graph and reading a

travel graph. From a set of numbers they should be able to calculate the mean.


23/46

19



Grade C

At this level, candidates are expected to show some insight into the mathematical structures of problems,

which enables them to justify generalisations, arguments or solutions. Mathematical presentation and

stages of derivations should be more extensive in order to generate fuller solutions. They should appreciate

the difference between mathematical explanation and experimental evidence.

Candidates should now apply the four rules of number to positive and negative integers, fractions

and decimal fractions, in order to solve problems. Percentage should be extended to problems

involving calculating one quantity as a percentage of another and its application to percentage change.

Calculations would now involve several operations and allow candidates to demonstrate fluent and

efficient use of calculators, as well as giving reasonable approximations. The relationship between

decimal and standard form of a number should be appreciated and applied to positive and negative

powers of 10. They should be familiar with the differences between simple and compound interest and

apply this to calculating both.

Candidates now need to extend their basic knowledge of sequences to recognise, and in simple cases

formulate, rules for generating a pattern or sequence. While extending the level of difficulty of solving

linear equations by involving appropriate algebraic manipulation, candidates are also expected to solve

simple simultaneous equations in two unknowns. Work with formulae extends into harder substitution

and evaluating the remaining term, as well as transforming simple formulae. The knowledge of basicalgebra is extended to the use of brackets and common factor factorisation. On graph work candidates

should be able to plot points from given values and use them to draw and interpret graphs in practical

situations, including travel and conversion graphs and algebraic graphs of linear and quadratic functions.

Candidates are expected to extend perimeter and area beyond rectilinear shapes to circles. They are

expected to appreciate and use area and volume units in relation to finding the volume and surface

area of a prism and cylinder. The basic construction work, with appropriate geometrical instruments,

should now be extended and applied to accurate scale diagrams to solve a two-dimensional problem.

Pythagoras theorem and trigonometry of right-angled triangles should be understood and applied

to solving, by calculation, problems in a variety of contexts. The calculation of angles in a variety

of geometrical figures, including polygons and to some extent circles should be expected from

straightforward diagrams.

Candidates should be able to use a frequency table to construct a pie chart. They need to understand

and construct a scatter diagram and apply this to a judgement of the correlation existing between two

quantities.


24/46

20



Grade A

At this level, candidates should make clear, concise and accurate statements, demonstrating ease and

confidence in the use of symbolic forms and accuracy or arithmetic manipulation. They should apply the

mathematics they know in familiar and unfamiliar contexts.

Candidates are expected to apply their knowledge of rounding to determining the bounds of intervals,

which may follow calculations of, for example, areas. They should understand and use direct and inverse

proportion. A further understanding of percentages should be evident by relating percentage change to

change to a multiplying factor and vice versa, e.g. multiplication by 1.03 results in a 3% increase.

Knowledge of the four rules for fractions should be applied to the simplification of algebraic fractions.

Building on their knowledge of algebraic manipulation candidates should be able to manipulate linear,

simultaneous and quadratic equations. They should be able to use positive, negative and fractional

indices in both numerical and algebraic work, and interpret the description of a situation in terms of

algebraic formulae and equations. Their knowledge of graphs of algebraic functions should be extended

to the intersections and gradients of these graphs.

The basic knowledge of scale factors should be extended to two and three dimensions and applied to

calculating lengths, areas and volumes between actual values and scale models. The basic right-handed

trigonometry knowledge should be applied to three-dimensional situations as well as being extended to

an understanding of and solving problems on non-right angled triangles.

At this level, candidates should be able to process data, discriminating between necessary and

redundant information. The basic work on graphs in practical situations should be extended to making

quantitative and qualitative deductions from distance/time and speed/time graphs.


25/46

21


5. Coursework: guidance for centres

The Coursework component provides candidates with an additional opportunity to show their ability in

Mathematics. This opportunity relates to all abilities covered by the Assessment Objectives, but especially

to the last five, where an extended piece of work can demonstrate ability more fully than an answer to a

written question.

Coursework should aid development of the ability

to solve problems,

to use mathematics in a practical way,

to work independently,

to apply mathematics across the curriculum,

and if suitable assignments are selected, it should enhance interest in, and enjoyment of, the subject.

Coursework assignments should form an integral part of both IGCSE Mathematics courses: whether some

of this Coursework should be submitted for assessment (syllabus 0581), or not (syllabus 0580), is a matter

for the teacher and the candidate to decide. A candidates Coursework grade cannot lower his or her overall

result.

5.1 Procedure(a) Candidates should submit one Coursework assignment.

(b) Coursework can be undertaken in class, or in the candidates own time. If the latter, the teacher must be

convinced that the piece is the candidates own unaided work, and must sign a statement to that effect

(see also Section 5.4 Controlled Elements).

(c) A good Coursework assignment is normally between 8 and 15 sides of A4 paper in length. These figures

are only for guidance; some projects may need to be longer in order to present all the findings properly,

and some investigations might be shorter although all steps should be shown.(d) The time spent on a Coursework assignment will vary, according to the candidate. As a rough guide,

between 10 and 20 hours is reasonable.


26/46

22



5.2 Selection of Coursework assignments(a) The topics for the Coursework assignments may be selected by the teacher, or (with guidance) by the

candidates themselves.

(b) Since individual input is essential for high marks, candidates should work on different topics. However,

it is possible for the whole class to work on the same topic, provided that account is taken of this in the

final assessment.

(c) Teachers should ensure that each topic corresponds to the ability of the candidate concerned. Topics

should not restrict the candidate and should enable them to show evidence of attainment at the highest

level of which they are capable. However, topics should not be chosen which are clearly beyond the

candidates ability.

(d) The degree of open-endedness of each topic is at the discretion of the teacher. However, each topic

selected should be capable of extension, or development beyond any routine solution, so as to give full

rein to the more imaginative candidate.

(e) The principal consideration in selecting a topic should be the potential for mathematical activity. With

that proviso, originality of topics should be encouraged.

(f) Some candidates may wish to use a computer at various stages of their Coursework assignment. This

should be encouraged, but they must realise that work will be assessed on personal input, and not what

the computer does for them. Software sources should be acknowledged.

5.3 Suggested topics for Coursework assignmentsGood mathematical assignments can be carried out in many different areas. It is an advantage if a suitable

area can be found which matches the candidates own interests.

Some suggestions for Coursework assignments are:

A mathematical investigation

There are many good investigations available from various sources: books, the Internet, etc. The

objective is to obtain a mathematical generalisation for a given situation.

At the highest level, candidates should consider a complex problem which involves the co-ordination of

three features or variables.


27/46

23



An application of mathematics

Packaging how can four tennis balls be packaged so that the least area of card is used?

Designing a swimming pool

Statistical analysis of a survey conducted by the candidate

Simulation games

Surveying taking measurements and producing a scale drawing or model

At the highest level, candidates should consider a complex problem which involves mathematics at

grade A. (See the section on grade descriptions.)

Teachers should discuss assignments with the candidates to ensure that they have understood what is

required and know how to start. Thereafter, teachers should only give hints if the candidate is completely

stuck.

Computer software packages may be used to enhance presentation, perform repetitive calculations or draw

graphs.

5.4 Controlled elements(a) The controlled element is included to assist the teacher in checking

(i) the authenticity of the candidates work,

(ii) the extent of the candidates learning of Mathematics, and its retention,

(iii) the depth of understanding of the Mathematics involved,

(iv) the ability to apply the learning to a different situation.

(b) The element must be carried out individually by the candidates under controlled conditions, but may take

any appropriate form, provided that the results are available for moderation, e.g.

a timed or untimed written test,

an oral exchange between the candidate and the teacher,

a parallel investigation or piece of work,

a parallel piece of practical work, or practical test including a record of the results,

a written summary or account.


28/46

24


6. Coursework assessment criteria

6.1 Scheme of assessment for Coursework

assignments(a) The whole range of marks is available at each level. The five classifications each have a maximum of 4

marks, awarded on a five-point scale, 0, 1, 2, 3, 4. For Coursework as a whole, including the controlled

element, a maximum of 20 marks is available. Participating schools should use the forms at the back of

the syllabus on which to enter these marks.(b) Assignments are part of the learning process for the candidates, and it is expected that they will receive

help and advice from their teachers. The marks awarded must reflect the personal contributions of the

candidates, including the extent to which they use the advice they receive in the development of the

assignments.

(c) The way in which the accuracy marks are allocated will vary from one assignment to another.

Numerical accuracy, accuracy of manipulation in algebra, accuracy in the use of instruments, care in

the construction of graphs and use of the correct units in measuring, are all aspects which may need

consideration in particular assignments.

(d) If a candidate changes his or her level of entry during the course, Coursework already completed

and assessed by the teacher will have to be reassessed according to the new entry option beforemoderation. A candidate being re-entered at the higher level (Extended curriculum) must be given the

opportunity to extend any assignment already completed before it is re-assessed.

(e) The use of ICT is to be encouraged; however, teachers should not give credit to candidates for the

skills needed to use a computer software package. For example, if data is displayed graphically by

a spreadsheet, then credit may be given for selecting the most appropriate graph to draw and for its

interpretation.

(f) Further information about the assessment of Coursework is given in the Coursework Training Handbook

and at training sessions.

The following tables contain detailed criteria for the award of marks from 0 to 4 under the five categories

of assessment (overall design and strategy, mathematical content, accuracy, clarity of argument and

presentation, controlled element). For the Coursework component as a whole, a maximum of 20 marks is

available.


29/46

25



Overall design and strategy

Assessment Criteria Core Extended

Much help has been received.

No apparent attempt has been made to plan the work0 0

Help has been received from the teacher, the peer group or a

prescriptive worksheet.

Little independent work has been done.

Some attempt has been made to solve the problem, but only at a simple

level.

The work is poorly organised, showing little overall plan.

1 0

Some help has been received from the teacher or the peer group.

A strategy has been outlined and an attempt made to follow it.

A routine approach, with little evidence of the candidate's own ideas

being used.

2 1

The work has been satisfactorily carried out, with some evidence of

forward planning.

Appropriate techniques have been used; although some of these may

have been suggested by others, the development and use of them is

the candidates own.

3 2

The work is well planned and organised.

The candidate has worked independently, devising and using techniques

appropriate to the task.

The candidate is aware of the wider implications of the task and has

attempted to extend it. The outcome of the task is clearly explained.

4 3

The work is methodical and follows a flexible strategy to cope with

unforeseen problems.

The candidate has worked independently, the only assistance received

being from reference books or by asking questions arising from the

candidates own ideas.

The problem is solved, with generalisations where appropriate.

The task has been extended and the candidate has demonstrated the

wider implications.

4 4


30/46

26



Mathematical content


Little or no evidence of any mathematical activity.

The work is very largely descriptive or pictorial.0 0

A few concepts and methods relevant to the task have been employed,

but in a superficial and repetitive manner. 1 0

A sufficient range of mathematical concepts which meet the basic needs

of the task has been employed.

More advanced mathematical methods may have been attempted, but

not necessarily appropriately or successfully.

2 1

The concepts and methods usually associated with the task have been

used, and the candidate has shown competence in using them.3 2

The candidate has used a wide range of Core syllabus mathematics

competently and relevantly, plus some mathematics from beyond the

Core syllabus.

The candidate has developed the topic mathematically beyond the usual

and obvious. Mathematical explanations are concise.

4 3

A substantial amount of work, involving a wide range of mathematical

ideas and methods of Extended level standard or beyond.

The candidate has employed, relevantly, some concepts and methods

not usually associated with the task in hand.

Some mathematical originality has been shown.

4 4


31/46


32/46

28



Clarity of argument and presentation


Haphazard organisation of work, which is difficult to follow. A series of

disconnected short pieces of work. Little or no attempt to summarise

the results.

0 0

Poorly presented work, lacking logical development.

Undue emphasis is given to minor aspects of the task, whilst important

aspects are not given adequate attention.

The work is presented in the order in which it happened to be

completed; no attempt is made to re-organise it into a logical order.

1 0

Adequate presentation which can be followed with some effort.

A reasonable summary of the work completed is given, though with

some lack of clarity and/or faults of emphasis.

The candidate has made some attempt to organise the work into a

logical order.

2 1

A satisfactory standard of presentation has been achieved.

The work has been arranged in a logical order.

Adequate justification has been given for any generalisations made.

The summary is clear, but the candidate has found some difficulty in

linking the various different parts of the task together.

3 2

The presentation is clear, using written, diagrammatic and graphical

methods as and when appropriate.

Conclusions and generalisations are supported by reasoned statementswhich refer back to results obtained in the main body of the work.

Disparate parts of the task have been brought together in a competent

summary.

4 3

The work is clearly expressed and easy to follow.

Mathematical and written language has been used to present the

argument; good use has been made of symbolic, graphical and

diagrammatic evidence in support.

The summary is clear and concise, with reference to the original aims;

there are also good suggestions of ways in which the work might beextended, or applied in other areas.

4 4


33/46

29



Controlled element


Little or no evidence of understanding the problem.

Unable to communicate any sense of having learned something by

undertaking the original task.

0 0

Able to reproduce a few of the basic skills associated with the task, but

needs considerable prompting to get beyond this.1 0

Can answer most of the questions correctly in a straightforward test on

the project.

Can answer questions about the problem and the methods used in its

solution.

2 1

Can discuss or write about the problem, in some detail.

Shows competence in the mathematical methods used in the work.

Little or no evidence of having thought about possible extensions to thework or the application of methods to different situations.

3 2

Can talk or write fluently about the problem and its solution.

Has ideas for the extension of the problem, and the applicability of the

methods used in its solution to different situations.

4 3 or 4*

*Dependent on the complexity of the problem and the quality of the ideas.


34/46

30



6.2 ModerationInternal Moderation

When several teachers in a Centre are involved in internal assessments, arrangements must be made within

the Centre for all candidates to be assessed to a common standard. It is essential that within each Centre

the marks for each skill assigned within different teaching groups (e.g. different classes) are moderated

internally for the whole Centre entry. The Centre assessments will then be subject to external moderation.

External Moderation

External moderation of internal assessment will be carried out by CIE. The internally moderated marks for

all candidates must be received at CIE by 30 April for the May/June examination and by 31 October for

the November examination. These marks may be submitted either by using MS1 mark sheets or by using

Cameo as described in the Handbook for Centres.

Once CIE has received the marks, CIE will select a sample of candidates whose work should be submitted

for external moderation. CIE will communicate the list of candidates to the Centre, and the Centre should

despatch the Coursework of these candidates to CIE immediately. Individual Candidate Record Cards

and Coursework Assessment Summary Forms (copies of which may be found at the back of this syllabus

booklet) must be enclosed with the Coursework.

Further information about external moderation may be found in the Handbook for Centresand the

Administrative Guide for Centres.


35/46

31


7. Appendix A

7.1 ResourcesCopies of syllabuses, the most recent question papers and Principal Examiners reports are available on the

Syllabus and Support Materials CD-ROM, which is sent to all CIE Centres.

Resources are also listed on CIEs public website at www.cie.org.uk. Please visit this site on a regular

basis as the Resource lists are updated through the year.

Access to teachers email discussion groups, suggested schemes of work and regularly updated resource

lists may be found on the CIE Teacher Support website at http://teachers.cie.org.uk . This website is

available to teachers at registered CIE Centres.


36/46

32


7. Appendix A

Forms:

Individual candidate record card

Coursework assessment summary form


37/46

MATHEMATICS

Individual Candidate Record Card

IGCSE 2012

Please read the instructions printed overleaf and the General Coursework Regulations before completing this form

Centre Number Centre Name June/Novem

Candidate Number Candidate Name Teaching Gr

Title(s) of piece(s) of work:

Classification of Assessment Use space below for Teachers comments

Overall design and strategy (max 4)

Mathematical content (max 4)

Accuracy (max 4)

Clarity of argument and presentation (max 4)

Controlled element (max 4)

Mark to be transferred to Coursework Assessment Summa

WMS329


38/46

INSTRUCTIONS FOR COMPLETING INDIVIDUAL CANDIDATE RECORD CARDS

1. Complete the information at the head of the form.

2. Mark the item of Coursework for each candidate according to instructions given in the Syllabus and Training Handbook

3. Enter marks and total marks in the appropriate spaces. Complete any other sections of the form required.

4. The column for teachers comments is to assist CIEs moderation process and should include a reference to the marksattention to particular features of the work are especially valuable to the Moderator.

5. Ensure that the addition of marks is independently checked.

6. It is essential that the marks of candidates from different teaching groups within each Centre are moderated in

awarded to all candidates within a Centre must be brought to a common standard by the teacher responsible for co-or

the internal moderator), and a single valid and reliable set of marks should be produced which reflects the relative atta

Coursework component at the Centre.

7. Transfer the marks to the Coursework Assessment Summary Form in accordance with the instructions given on that d

8. Retain all Individual Candidate Record Cards and Coursework which will be required for external moderation. Furth

moderation will be sent in late March of the year of the June Examination and in early October of the year of the Nove

instructions on the Coursework Assessment Summary Form.

Note:These Record Cards are to be used by teachers only for candidates who have undertaken Coursework as part of the


39/46

MATHEMATICS

Coursework Assessment Summary Form

IGCSE 2012

Please read the instructions printed overleaf and the General Coursework Regulations before completing this fo

Centre Number Centre Name June/No

Candidate

Number

Candidate Name Teaching

Group/

Set

Title(s) of piece(s) of work

Name of teacher completing this form Signature

Name of internal moderator Signature

WMS330


40/46

A. INSTRUCTIONS FOR COMPLETING COURSEWORK ASSESSMENT SUMMARY FORMS

1. Complete the information at the head of the form.

2. List the candidates in an order which will allow ease of transfer of information to a computer-printed Coursewor

candidate index number order, where this is known; see item B.1 below). Show the teaching group or set for e

be used to indicate group or set.

3. Transfer each candidates marks from his or her Individual Candidate Record Card to this form as follows:(a) Where there are columns for individual skills or assignments, enter the marks initially awarded (i.e. before in

(b) In the column headed Total Mark, enter the total mark awarded before internal moderation took place.

(c) In the column headed Internally Moderated Mark, enter the total mark awarded afterinternal moderation to

4. Both the teacher completing the form and the internal moderator (or moderators) should check the form and co

B. PROCEDURES FOR EXTERNAL MODERATION

1. University of Cambridge International Examinations (CIE) sends a computer-printed Coursework mark sheet MS

examination and in early October for the November examination) showing the names and index numbers of eac

moderated mark for each candidate from the Coursework Assessment Summary Form to the computer-printed

2. The top copy of the computer-printed Coursework mark sheet MS1 must be despatched in the specially provide

CIE but no later than 30 April for the June examination and 31 October for the November examination.

3. CIE will select a list of candidates whose work is required for external moderation. As soon as this list is receiv

corresponding Individual Candidate Record Cards, this summary form and the second copy of the computer-prin

the candidates who are in the sample by means of an asterisk (*) against the candidates names overleaf.

4. CIE reserves the right to ask for further samples of Coursework.

5. If the Coursework involves three-dimensional work then clear photographs should be submitted in place of the a


41/46

37


8. Appendix B: Additional information

Guided learning hoursIGCSE syllabuses are designed on the assumption that candidates have about 130 guided learning hours

per subject over the duration of the course. (Guided learning hours include direct teaching and any other

supervised or directed study time. They do not include private study by the candidate.)

However, this figure is for guidance only, and the number of hours required may vary according to local

curricular practice and the candidates prior experience of the subject.

Recommended prior learningWe recommend that candidates who are beginning this course should have previously studied an

appropriate lower secondary Mathematics programme.

ProgressionIGCSE Certificates are general qualifications that enable candidates to progress either directly to

employment, or to proceed to further qualifications.

Candidates who are awarded grades C to A* in IGCSE Extended tier Mathematicsare well prepared to

follow courses leading to AS and A LevelMathematics, or the equivalent.

Component codesBecause of local variations, in some cases component codes will be different in instructions about making

entries for examinations and timetables from those printed in this syllabus, but the component names will

be unchanged to make identification straightforward.

Grading and reportingIGCSE results are shown by one of the grades A*, A, B, C, D, E, F or G indicating the standard achieved,

Grade A* being the highest and Grade G the lowest. Ungraded indicates that the candidates performance

fell short of the standard required for Grade G. Ungraded will be reported on the statement of results but

not on the certificate. For some language syllabuses CIE also reports separate oral endorsement grades ona scale of 1 to 5 (1 being the highest).

Percentage uniform marks are also provided on each candidates Statement of Results to supplement their

grade for a syllabus. They are determined in this way:

A candidate who obtains

the minimum mark necessary for a Grade A* obtains a percentage uniform mark of 90%.

the minimum mark necessary for a Grade A obtains a percentage uniform mark of 80%.

the minimum mark necessary for a Grade B obtains a percentage uniform mark of 70%.

the minimum mark necessary for a Grade C obtains a percentage uniform mark of 60%. the minimum mark necessary for a Grade D obtains a percentage uniform mark of 50%.


42/46

38


8. Appendix B: Additional information

the minimum mark necessary for a Grade E obtains a percentage uniform mark of 40%.

the minimum mark necessary for a Grade F obtains a percentage uniform mark of 30%.

the minimum mark necessary for a Grade G obtains a percentage uniform mark of 20%.

no marks receives a percentage uniform mark of 0%.

Candidates whose mark is none of the above receive a percentage mark in between those stated according

to the position of their mark in relation to the grade thresholds (i.e. the minimum mark for obtaining a

grade). For example, a candidate whose mark is halfway between the minimum for a Grade C and the

minimum for a Grade D (and whose grade is therefore D) receives a percentage uniform mark of 55%.

The uniform percentage mark is stated at syllabus level only. It is not the same as the raw mark obtained

by the candidate, since it depends on the position of the grade thresholds (which may vary from one session

to another and from one subject to another) and it has been turned into a percentage.

ResourcesCopies of syllabuses, the most recent question papers and Principal Examiners reports are available on the

Syllabus and Support Materials CD-ROM, which is sent to all CIE Centres.

Resources are also listed on CIEs public website at www.cie.org.uk. Please visit this site on a regular

basis as the Resource lists are updated through the year.

Access to teachers email discussion groups, suggested schemes of work and regularly updated resource

lists may be found on the CIE Teacher Support website at http://teachers.cie.org.uk . This website is

available to teachers at registered CIE Centres.


43/46

39


9.Appendix C: Additional information Cambridge International Certificates

The Mathematics 0580 syllabus is accredited for use in England, Wales and Northern Ireland.

Additional information on this accredited version is provided below.

Prior LearningCandidates in England who are beginning this course should normally have followed the Key Stage 3

programme of study within the National Curriculum for England.

Other candidates beginning this course should have achieved an equivalent level of general education.

NQF LevelThis qualification is accredited by the regulatory authority for England, Ofqual, as part of the National

Qualifications Framework as a Cambridge International Level 1/Level 2 Certificate.

Candidates who gain grades G to D will have achieved an award at Level 1 of the National Qualifications

Framework.

Candidates who gain grades C to A* will have achieved an award at Level 2 of the National Qualifications

Framework.

ProgressionCambridge International Level 1/Level 2 Certificates are general qualifications that enable candidates to

progress either directly to employment, or to proceed to further qualifications.

This syllabus provides a foundation for further study at Levels 2 and 3 in the National Qualifications

Framework, including GCSE, AS and A Level GCE, and Cambridge Pre-U qualifications.

Candidates who are awarded grades C to A* are well prepared to follow courses leading to Level 3 AS and A

Level GCE Mathematics, Cambridge Pre-U Mathematics, IB Mathematics or the Cambridge International AS

and A Level Mathematics.

Guided Learning HoursThe number of guided learning hours required for this course is 130.

Guided learning hours are used to calculate the funding for courses in state schools in England, Wales and

Northern Ireland. Outside England, Wales and Northern Ireland, the number of guided learning hours should

not be equated to the total number of hours required by candidates to follow the course as the definition

makes assumptions about prior learning and does not include some types of learning time.


44/46

40


9.Appendix C: Additional information Cambridge International Certificates

Overlapping QualificationsCentres in England, Wales and Northern Ireland should be aware that every syllabus is assigned to a national

classification code indicating the subject area to which it belongs. Candidates who enter for more than one

qualification with the same classification code will have only one grade (the highest) counted for the purpose

of the school and college performance tables.

The classification code for this syllabus is 2210.

Spiritual, ethical, social, legislative, economic and cultural issues

Spiritual: There is the opportunity for candidates to appreciate the concept of truth in a mathematical context

and to gain an insight into how patterns and symmetries rely on underlying mathematical principles.

Moral: Candidates are required to develop logical reasoning, thereby strengthening their abilities to make

sound decisions and assess consequences; they will also appreciate the importance of persistence in

problem solving.

Ethical: Candidates have the opportunity to develop an appreciation of when teamwork is appropriate and

valuable, but also to understand the need to protect the integrity of individual achievement.

Social: There is the opportunity for candidates to work together productively on complex tasks and to

appreciate that different members of a team have different skills to offer.

Cultural: Candidates are required to apply mathematics to everyday situations, thereby appreciating its

central importance to modern culture; by understanding that many different cultures have contributed to

the development of mathematics and that the language of mathematics is universal, candidates have the

opportunity to appreciate the inclusive nature of mathematics.

Sustainable development, health and safety considerations and

international developmentsThis syllabus offers opportunities to develop ideas on sustainable development and environmental issues

and the international dimension.

Sustainable development and environmental issues

Issues can be raised and addressed by questions set in context (e.g. pie charts; bar charts; optimising

resources).

The International dimension

Questions are set using varied international contexts (maps; currencies; journeys) and with cultural

sensitivity.

Avoidance of biasCIE has taken great care in the preparation of this syllabus and assessment materials to avoid bias of any

kind.


45/46


46/46

University of Cambridge International Examinations

1 Hills Road, Cambridge, CB1 2EU, United Kingdom

Tel: +44 (0)1223 553554 Fax: +44 (0)1223 553558

Maths With Out Coursework (2012)

Documents

Transcript of Maths With Out Coursework (2012)